Linearized polynomials attracted a lot of attention because of their applications to construct MRD codes [1]}, to study list decodability of rank metric codes [2]}, [3]}, [4]}, cyclic subspace codes [5]}, [6]} and affine dispersers [7]} and Elliptic curve discrete logarithm problem [8]}.
Motivated by these applications, we further investigated the results on linearized trinomials with maximum kernel of [9]}.
More precisely, we first refine their results for \(\sigma \) -polynomials proving the following.
